Currently, there are three commonly used steering laws that are used for low-thrust transfer-orbit missions for spacecrafts. These three prior art steering laws are depicted in FIGS. 1A, 1B, and 1C. These three steering methodologies are used to determine the direction of the in-plane component of acceleration to be applied to the spacecraft during a transfer orbit mission. Specifically, FIG. 1A shows the steering law for an acceleration component that is perpendicular to the line of apoapse (⊥a; fixed inertial); FIG. 1B shows the steering law for an acceleration component that is perpendicular to the radius vector (⊥r); and FIG. 1C shows the steering law for an acceleration component that is along the velocity/anti-velocity vector (∥v). The applicability of any of these three steering laws for a transfer orbit mission is a function of the initial orbit of the spacecraft.
Each of these three prior art steering laws is used to achieve a specific orbit objective. In particular, the steering law depicted in FIG. 1A is used for targeting the orbital eccentricity, and the steering laws depicted in FIGS. 1B and 1C are used for targeting the orbital semi-major axis. With a few exceptions, these steering laws and their objectives are exclusive of each other and, thus, there is a conflict between them when it is desirable to achieve targets for the semi-major axis and the orbit eccentricity parameters (as well as the orbit inclination parameter for out-of-plane cases). For this reason, a typical solution and practice is to divide the mission into distinct phases, with each phase employing a different steering law, in order to achieve the respective orbital targets. As such, the total mission duration is the sum of the duration of each phase that is performed for the mission. The total mission duration can be relatively long when the orbital parameters (i.e. the orbit eccentricity, the semi-major axis, and/or the orbit inclination of the initial orbit) are far from their targets. In addition, it should be noted that switching between different steering strategies during the mission requires reconfiguration of the spacecraft's control systems and large changes to the spacecraft's orientation. Thus, frequent switching between steering laws in every orbit or between different phases during transfer orbit poses operational complexities, including a significant amount of down or no-burn time, which renders the existing solution cumbersome.